The generator matrix

 1  0  0  0  1  1  1  1  1  1  1  1 2X 4X  1  1  1  1  1  1 3X  1  1  1  1  1  1  1  X  1  1  1 2X  1  1  X  1 4X  1  1  1 2X  1  1  1  1  1  1  X  1  1  1  1  1  1  X  1  1  1  1  1 2X  1  1  1  1  1  1  0  1  1  1  1 3X 4X  1
 0  1  0  0 3X 4X 3X+1 4X+1  1 3X+2  4 3X+3  1  1 2X+4 X+4 3X+4 X+1  0 2X+3  1 2X+4  2 X+3 2X+2 2X+3  4 3X+1  1 3X+3 X+1 4X+3  1 3X+1 3X  1 2X+1  X  3  3  X  1 4X+4 X+1 2X+2 X+3 X+4  2  1 4X+2  0 4X+3 4X+4 3X+3 X+1  1  1 3X+2 2X+3 3X+4 2X+1  X X+4 3X+4 2X+1  2 3X+2 3X+3  1 3X  X X+1 2X  1  1 X+1
 0  0  1  0 3X+1 3X+2 3X+3  1 4X+2 X+1  2 2X+3 3X+2 2X+3 2X+1 X+3 3X 3X+4 4X+4  2 X+4  1 4X+2  4  2  0 X+4  X  4 2X+2 2X 4X+1 X+2 4X+2 X+3 X+1 4X+1  1 2X+3  X 4X+1 3X+3 2X+4  X 4X 4X 2X+4  4 3X X+3 3X+4  3 3X+3 4X 2X+2  X X+3  3 3X+4 4X 3X+1  1 2X+3 3X+2 3X+2 4X+3 2X+4 3X+1 2X+2  2 X+2  4  3 4X+4  0 X+4
 0  0  0  1 3X+3 3X+2 4X+3 3X+1  X 4X+2 X+1 2X X+4  2  4 4X+4 4X+1 2X+1 3X+4 3X+2 3X  3 3X  3 2X+4 4X  1 4X+4  2 4X+3 X+2 4X+1 4X+3 X+4 4X+2 2X+3  0 3X+4 4X+1 X+4  2  0  3 2X+3  2 X+3 2X+2 2X 3X+2 2X+4 2X+2  4 X+3 2X+1  2 3X+3 X+1 2X+1 4X+1 4X+2  3 3X+3 X+2 2X X+1 4X+3 X+4 X+3 3X  2 2X+1 2X+1 X+4 4X+3 2X+1 X+3

generates a code of length 76 over Z5[X]/(X^2) who´s minimum homogenous weight is 283.

Homogenous weight enumerator: w(x)=1x^0+1020x^283+1080x^284+1480x^285+2540x^286+1940x^287+4880x^288+3680x^289+4236x^290+6540x^291+4900x^292+9600x^293+8320x^294+8472x^295+12660x^296+8820x^297+16380x^298+13440x^299+12644x^300+19300x^301+10680x^302+24320x^303+19420x^304+17384x^305+21300x^306+12120x^307+23660x^308+19720x^309+14872x^310+18160x^311+9520x^312+17260x^313+9800x^314+7464x^315+8260x^316+3800x^317+4900x^318+2040x^319+1508x^320+1240x^321+720x^322+480x^323+24x^325+20x^330+12x^335+4x^340+4x^345

The gray image is a linear code over GF(5) with n=380, k=8 and d=283.
This code was found by Heurico 1.16 in 589 seconds.